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We establish a Liouville-type theorem for a subcritical nonlinear problem,involving a fractional power of the sub-Laplacian in the Heisenberg group. Toprove our result we will use the local realization of fractional CR covariantoperators, which can be constructed as the Dirichlet-to-Neumann operator of adegenerate elliptic equation in the spirit of Caffarelli and Silvestre, asestablished in \cite{FGMT}. The main tools in our proof are the CR inversionand the moving plane method, applied to the solution of the lifted problem inthe half-space $\mathbb H^n\times \mathbbR^+$.

A nonlinear Liouville theorem for fractional equations in the Heisenberg group